$A$ $B$ $C$ If: $ AC = 40$, $ AB = 3x + 4$, and $ BC = 6x + 9$, Find $BC$.
Explanation: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {3x + 4} + {6x + 9} = {40}$ Combine like terms: $ 9x + 13 = {40}$ Subtract $13$ from both sides: $ 9x = 27$ Divide both sides by $9$ to find $x$ $ x = 3$ Substitute $3$ for $x$ in the expression that was given for $BC$ $ BC = 6({3}) + 9$ Simplify: $ {BC = 18 + 9}$ Simplify to find ${BC}$ : $ {BC = 27}$